In the triangle ABC, D and E are the midpoint of BC and AC respectively, ad and be intersect at O. given that the area of triangle ABC is 1, calculate the area of triangle BOD

In the triangle ABC, D and E are the midpoint of BC and AC respectively, ad and be intersect at O. given that the area of triangle ABC is 1, calculate the area of triangle BOD

This topic should first make two auxiliary lines, which will be easier to understand. The steps are as follows: 1. Make the third middle line CF of the triangle, connect FD, and intersect be at m2. Theorem: any middle line of the triangle bisects the area of the triangle. 3. FD is the line connecting the midpoint, so FD is parallel to AC, and FD = 1 / 2Ac, M is the midpoint of FD

[urgent] center of gravity: in △ ABC, the middle line AD and the middle line be intersect at point O. if the area of △ BOD is 2, calculate the area of △ ABC
Using the knowledge of the center of gravity in the second grade of junior high school: in △ ABC, the intersection point of the middle line AD and the middle line be is o. if the area of △ BOD is 2, the area of △ ABC can be calculated

The fastest way is to take a special equilateral triangle;
General solution:
The ratio of the distance from the center of gravity to the vertex and the distance from the center of gravity to the midpoint of the opposite side is 2:1
Ao = 2od; △ AOB is equal to △ DOB, so the area of triangle AOB is equal to twice △ BOD, that is 4
The area of △ abd is 6
And D is the midpoint of BC, so the area of △ ABC is equal to twice of △ abd, which is 12

In the triangle ABC, take a point F, D, E on each side of AB, BC, AC, connect ad, be, CF, the intersection point is O, the known triangle AFO, BOD, ODC, EOC area is respectively
216,80,40,45 to calculate the area of OFB and AOE?

SBOD=80 SODC=40 DB=2DC SOFB=x SEOC=y (216+y)/(45+x)=2
120/(y+216)=45/x x=135 y=144